Question
Differentiate.
f(x) = 8 − x^ex/x + ex
f '(x) =
f(x) = 8 − x^ex/x + ex
f '(x) =
Answers
Steve
Hard to tell just what you mean there. If you mean
f(x) = (8-xe^x)/(x+e^x)
f' = [(-e^x - xe^x)(x+e^x) - (8-xe^x)(1+e^x)]/(x+e^x)^2
= (-xe^x - x^2 e^x - e^2x - xe^2x - 8 + xe^x - 8e^x + xe^2x)/(x+e^x)^2
= (e^x(-x+x^2-e^x-xe^x+x-8+xe^x)-8)/(x+e^x)^2
= (e^x(x^2-e^x-8)-8)/(x+e^x)^2
doesn't get much simpler
If I got the original wrong, fix it and visit wolframalpha.com
f(x) = (8-xe^x)/(x+e^x)
f' = [(-e^x - xe^x)(x+e^x) - (8-xe^x)(1+e^x)]/(x+e^x)^2
= (-xe^x - x^2 e^x - e^2x - xe^2x - 8 + xe^x - 8e^x + xe^2x)/(x+e^x)^2
= (e^x(-x+x^2-e^x-xe^x+x-8+xe^x)-8)/(x+e^x)^2
= (e^x(x^2-e^x-8)-8)/(x+e^x)^2
doesn't get much simpler
If I got the original wrong, fix it and visit wolframalpha.com